By what reason that khilafat movement …

As per Ncert 

The Khilafat Movement was started to save the Ottoman Empire and it extended to India against the British power. During the 1st world war, Turkey helped Germany to war against British.The Khilafat Movement expanded to South Asia under the leadership of ali brothers.

*The Khilafat Movement in India got the support of Mahatma Gandhim.Gandhiji advised the Muslim leaders to start non-cooperation with the British to force them to re-establish Khilafat.

Extra info not as per Ncert.

in 1920 British imposed a harsh treaty on the Turkish sultan or khilafat.

people got furious about this as they have been about the jalianwala bagh massacre .

also Indian Muslims were keen that khilafa be allowed to control over Muslim sacred places.

as British removed khilafat to control over sacred places khilafat movement was started.